Question

Consider the following hypothesis test.

H₀: μ ≤ 12

H_a: μ > 12

A sample of 25 provided a sample mean

x = 14 and a sample standard deviation s = 4.32.

(a) Compute the value of the test statistic. (Round your answer to three decimal places.) _______

(b)

Use the t distribution table to compute a range for the p-value.

a) p-value > 0.200

b) 0.100 < p-value < 0.200

c) 0.050 < p-value < 0.100

d) 0.025 < p-value < 0.050

e) 0.010 < p-value < 0.025

d) p-value < 0.010

(C)

At

α = 0.05,

what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that μ > 12.

Reject H₀. There is sufficient evidence to conclude that μ > 12.     

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

Reject H₀. There is insufficient evidence to conclude that μ > 12.

(D)

What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.)

test statistic ≤ ____

test statistic ≥ _____

What is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that μ > 12.

Reject H₀. There is sufficient evidence to conclude that μ > 12.     

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

Reject H₀. There is insufficient evidence to conclude that μ > 12.

Answer 1

Here we have: 14 S = 4.32 α 0.05 Hypothesis: Ho.IS 12 Hai μ > 12 a) (σ unknown) Test statistics: t-distribution x-μ - 14-12-2315 -= 2.315 4.32 /25

df = n-1 = 25-1 = 24 b) P-value- p (t>|2.315) 0.0147 Correct option "E" e) 0.010 p-value<0.025 Correct option "B" Reject Ho. There is sufficient evidence to conclude that μ > 12 d). Critical value tcrit ta,dftoo5,24-1.711 test statistics 2 1.711 Conclusion: Reject Ho. There is sufficient evidence to conclude that μ > 12.